Excerpts from: Kent’s Mechanical Engineering Handbook
When direct noise, containing definite notes or harmonics, is transmitted along ducts or openings, it often is possible to eliminate objectionable harmonics completely by an acoustic filter that obstructs but little air flow or ventilation.
Sound filters are of two classes:
1) low-pass filters – which transmit low frequencies, but filter out higher ones; and
2) high-pass filters – which do the opposite.
A low-pass filter prevents transmission of the relatively high whistle often present in a ventilating duct. Low frequencies, predominant in explosive discharges, are filtered out by a high-pass filter, as an automotive muffler or Maxim silencer.
Space is the usual limitation in filter applications, restricting for low-pass filters less than high-pass. Low-pass filters return sound energy to the source, where it dissipates itself through reflections, etc. High-pass filters must themselves dissipate the sound, this being important reason for their comparative bulk. The individual stages of a filter must be considerably shorter than the wavelength of sound being filtered, each stage producing a definite amount of attenuation, as illustrated by the specific design which follow.
LOW-PASS FILTERS may be divided into two classes of design:
1) Type 1 Low-pass acoustic filter
2) Type 2 Low-pass acoustic filter
The filtering action of type 1 low-pass filter covers a broader range of frequency than type 2 and is very efficient. Type 2, however, can sometimes be designed to occupy considerably less space than type 1. The preferred type depends on conditions to be met.
HIGH-PASS FILTERS are not so efficient in performance as low-pass filters and are, as a rule, more bulky. This type of filter functions through successive side leakage of pressure waves as they pass through the tube. When the wave escapes from the tube end, its pressure amplitude and its intensity are greatly reduced. An appreciable amount of sound, however, escapes through the side holes. Good high-pass filters require an outer shell of considerably larger diameter than the inner tube, the interspace being stuffed with damping material such as metal wool or asbestos fibers. Steel wool will rust in gas-engine exhaust mufflers.
Fig. 3. Explosion muffler
Figure 3 is a cross section of an efficient muffler that has considerably less back pressure than the baffle-type automotive muffler. For high attenuation, many small holes are better than the few large ones of figure 2. This type of filter always attenuate low-frequency impulse waves.
PERFORMANCE. An ideal sound filter produces a certain percentage drop in sound intensity per stage for every frequency within its range of attenuation. Thus, a six stage low-pass filter may attenuate a 300-cycle tone by 4 db per stage, or 24 db in all. A sharply tuned type 2 low-pass filter will attenuate much more. Attenuation in decibels per stage is independent of the initial sound intensity.
Performance of a low-pass filter sometimes is disappointing. Tube-resonance effects must be avoided. A tube of length equal to a multiple of one-half the wavelength of sound of a given frequency will resonate to that frequency. An otherwise well-designed filter may not perform well if such effects enter; placing it in different positions in the duct usually will eliminate them. High-pass filters, as mufflers, are less subject to this trouble. A fairly good knowledge of the elementary principles of sound is desirable in making sound-filter applications.
The following are my concept muffler design, it may be practical or not. Not yet tested in real life situation.
Fig. 4. 1-into-2 Explosion muffler
Fig. 5. Explosion muffler with diffuser
Note: For the formulas in designing acoustic filter and other information, please refer to the book Kent’s Mechanical Engineering Handbook.